Zachary Easterly -- the now-fired, ex-GlaxoSmithKline-employee -- alluded to being racist in the first video we got of him freaking out ... and now, we have the proof. Here's new video, obtained by TMZ, showing him on Tuesday throwing the epithet around like it was a frisbee.

This clip picks up with him being escorted off the plane, and he's literally dropping the N-word left and right -- in front of Black airline employees, no less -- with no shame.

As others hear him on his way out -- now entering the main terminal area of the airport -- he starts to get accosted and confronted by outraged bystanders ... who tell him to watch his mouth, or suffer the consequences. He chose to do the latter, and all hell broke loose.

Two men are seen tussling with Easterly at one point, and they even pin him down onto the ground -- seemingly in an attempt to make a citizen's arrest ... you can hear them talk about police/security. It's unclear if Easterly was ever detained or arrested, however. Philadelphia PD tells us they're looking into whether a case was opened in this matter or not.

What we do know is that he's without a job ... as GSK canned this man shortly after the video was posted and went viral. Once a proud chemist, now some jackass on the internet.

Easterly had suggested he was somewhat intoxicated during this, but that's obviously no excuse ... sounds like he got some things off his chest that he'd been holding in a long time.